(CNN) -- The top two seeds, Dinara Safina and Serena Williams, are both through to the second round of the China Open in Beijing after claiming straight sets victories on Sunday.

Williams will become the new world number one if she betters Dinara Safina's result in Beijing.

Williams did not have things all her own way as she defeated Estonia's Kaia Kanepi 7-5 6-4 while Safina -- looking to bounce back after an embarrassing loss last week in Japan --beat Italy's Roberta Vinci 6-4 6-4.

"It was a good challenging match to start out with. It wasn't easy but I felt like I was hitting a clean ball," Williams told reporters.

The 23-year-old Safina will now face Chinese wild card Zhang Shuai in the second round, while Williams takes on Russia's Ekaterina Makarova.

Williams needs to have a better result than Safina in Beijing to claim the number one ranking from her Russian rival.

In other matches, sixth seed Svetlana Kuznetsova survived a scare from China's Zheng Jie before edging through 7-6 7-5, while there were also wins for seventh seed Vera Zvonareva and ninth seed Victoria Azarenka of Belarus.